Question

Please help me with this question that were stuck on I am trying to help my son to understand but I am having trouble with breaking this down. He brought it back home from getting it wrong please help. I have attached a picture of the problemUse the linear combination method to solve the system of equations. Explain each step of your solution.2x – 3y = 133x + y = -8

Answer 1

The given equations are

$2x-3y=13\text{ take it as equation (1).}$$3x+y=-8\text{ take it as equation (2).}$

We need to eliminate one variable by adding and subtracting the equations.

First, multiply equation (1) by 3 as follows.

$3\times2x-3\times3y=3\times13\text{ }$

$6x-9y=39\text{ take it as equation (3).}$

Multiplying equation (2) by (-2) , we get

$(-2)3x+(-2)y=-(-2)8$

$-6x-2y=16\text{ take it as equation (4).}$

Add equation (3) and equation (4) to eliminate the x variable.

$(6x-9y)+(-6x-2y)=39+16$

$6x-9y-6x-2y=39+16$

$-11y=55$

Dividing both sides by (-110, we get

$-\frac{11y}{-11}=\frac{55}{-11}$$y=-5$

We get y=-5.

Substitute y=-5 in the equation (1), to find the value of x.

$2x-3(-5)=13$

$2x+15=13$

Subtracting 15 from both sides of the equation, we get

$2x+15-15=13-15$

$2x=-2$

Dividing both sides by 2, we get

$\frac{2x}{2}=-\frac{2}{2}$$x=-1$

Hence the solution is

$x=-1\text{ and }y=-5$